Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
216 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C16 | D97 |
| commutator, hypocenter | C97 | C2×C4×C16 |
| Frattini | C2×C8 | C22×D97 |
| Fitting | C4×C16×C97 | C2 |
| socle | C22×C97 | C22×C8 |
| prime radical | C22×D97 | C2×C8 |
| cosocle | C2×C8×C97 | C23 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C4×C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×#13095486 | C2 | semidirect |
| 4. C16×Dic97 | C2 | semidirect |
| 5. C4×C16×C97 | C2 | semidirect |
| 10. C16×D97 | C4 | direct (N × H) |
| 24. #13095486 | C2×C4 | semidirect |
| 28. C16×C97 | C2×C4 | semidirect |
| 34. C4×D97 | C16 | direct (N × H) |
| 44. C4×C97 | C2×C16 | semidirect |
| 48. Dic97 | C2×C16 | semidirect |
| 51. D97 | C4×C16 | direct (N × H) |
| 53. C97 | C2×C4×C16 | semidirect |
| 58. C4×C16 | D97 | direct (N × H) |
| 81. C16 | C4×D97 | direct (N × H) |
| 99. C4 | C16×D97 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D97 | 2 |
| C4×C8×D97 | 2 |
| C4×#13095486 | 2 |
| C16×Dic97 | 2 |
| C4×C16×C97 | 2 |
| C2×C4×C16 | 97 |